Affix

suffixaffixesaffixationsuffixesprefixsuffixes or prefixesadfixaffix morphemesaffixationalaffixes.
In linguistics, an affix is a morpheme that is attached to a word stem to form a new word or word form.wikipedia
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Morpheme

morphemesmorphemicderivational
In linguistics, an affix is a morpheme that is attached to a word stem to form a new word or word form.
When it depends on another morpheme to express an idea, it is an affix because it has a grammatical function (such as the –s in cats to indicate that it is plural).

Prefix

prefixesprefixationquasi-
They are bound morphemes by definition; prefixes and suffixes may be separable affixes.
A prefix is an affix which is placed before the stem of a word.

Suffix

suffixesendingsuffixation
They are bound morphemes by definition; prefixes and suffixes may be separable affixes.
In linguistics, a suffix (sometimes termed postfix) is an affix which is placed after the stem of a word.

Inflection

inflectedinflectional morphologyinflectional
Affixes may be derivational, like English -ness and pre-, or inflectional, like English plural -s and past tense -ed.
An inflection expresses grammatical categories with affixation (such as prefix, suffix, infix, circumfix, and transfix), apophony (as Indo-European ablaut), or other modifications.

Infix

infixesinfixationinfixed
An infix is an affix inserted inside a word stem (an existing word, or the core of a family of words).

Bound and free morphemes

bound morphemefree morphemebound
They are bound morphemes by definition; prefixes and suffixes may be separable affixes.
Affixes are bound by definition.

Linguistics

linguistlinguisticlinguists
In linguistics, an affix is a morpheme that is attached to a word stem to form a new word or word form.
The lexicon consists of words and bound morphemes, which are parts of words that can't stand alone, like affixes.

Morphological derivation

derivationderivationalderived
Affixes may be derivational, like English -ness and pre-, or inflectional, like English plural -s and past tense -ed.
Derivational morphology often involves the addition of a derivational suffix or other affix.

Circumfix

circumfixes
A circumfix (abbreviated ) (also confix or ambifix) is an affix which has two parts, one placed at the start of a word, and the other at the end.

Compound (linguistics)

compoundcompound wordcompounds
The addition of affix morphemes to words (such as suffixes or prefixes, as in employ → employment) should not be confused with nominal composition, as this is actually morphological derivation.

Suprafix

In linguistics, a suprafix is a type of affix that gives a suprasegmental pattern (such as tone, stress, or nasalization) to either a neutral base or a base with a preexisting suprasegmental pattern.

Transfix

In linguistic morphology, a transfix is a discontinuous affix which is inserted into a word root, as in root-and-pattern systems of morphology, like those of many Semitic languages.

Simulfix

In linguistics, a simulfix is a type of affix that changes one or more existing phonemes (usually vowels) in order to modify the meaning of a morpheme.

Reduplication

reduplicatedreduplicativereduplicating
However, reduplication often occurs with other phonological and morphological process, such as deletion, affixation of non-reduplicating material, etc.

Grammaticalization

grammaticalizedgrammaticalisationgrammaticalised
In other cases, the lexical suffixes have become grammaticalized to various degrees.
In historical linguistics and language change, grammaticalization (also known as grammatization or grammaticization) is a process of language change by which words representing objects and actions (i.e. nouns and verbs) become grammatical markers (affixes, prepositions, etc.).

Definiteness

definiteindefinitedef.
Note how the lexical suffix is neither "the baby" (definite) nor "a baby" (indefinite); such referential changes are routine with incorporated nouns.
In yet other languages, definiteness is indicated by affixes on the noun or on modifying adjectives, much like the expression of grammatical number and grammatical case.

Classical compound

combining formscombining formneoclassical compound
Classical compounds and neoclassical compounds are compound words composed from combining forms (which act as affixes or stems) derived from classical Latin or ancient Greek roots.

Clitic

encliticprocliticenclitics
A clitic is pronounced like an affix, but plays a syntactic role at the phrase level.

List of family name affixes

Family name affixesfamily name suffixes-in
Family name affixes are a clue for surname etymology and can sometimes determine the ethnic origin of a person.

Halkomelem

HalqemeylemHalkomelem languageHalq'eméylem
Gerdts (2003) gives examples of lexical suffixes in the Halkomelem language (the word order here is verb–subject–object):

Marker (linguistics)

markermarkerscase marker
Most characteristically, markers occur as clitics or inflectional affixes.

Auxiliary verb

auxiliaryauxiliary verbsauxiliaries
(The niʔ here is an auxiliary, which can be ignored for explanatory purposes.)
Other languages, such as Latin, are synthetic, which means they tend to express functional meaning with affixes, not with auxiliary verbs.

Stemming

word stemmingstemmedStemmer
In linguistics, the term affix refers to either a prefix or a suffix.